An Iterative Method for the Least-Squares Problems of a General Matrix Equation Subjects to Submatrix Constraints

作者：Dai Li fang^*; Liang Mao lin; Shen Yong hong

来源：Journal of Applied Mathematics, 2013, 2013: 697947.

DOI：10.1155/2013/697947

An iterative algorithm is proposed for solving the least-squares problem of a general matrix equation Sigma(t)(t=1) M(i)Z(i)N(i) = F, where Z(i) (i - 1, 2, ... ,t) are to be determined centro-symmetric matrices with given central principal submatrices. For any initial iterative matrices, we show that the least-squares solution can be derived by this method within finite iteration steps in the absence of roundoff errors. Meanwhile, the unique optimal approximation solution pair for given matrices (Z) over bar (i) can also be obtained by the least-norm least-squares solution of matrix equation Sigma(t)(t=1) M-i(Z) over bar N-i(i) = (F) over bar, in which (Z) over bar (i) = Z(i) - (Z) over bar (i), (F) over bar = F - Sigma(t)(t=1) M-i(Z) over bar N-i(i). The given numerical examples illustrate the efficiency of this algorithm.

• 出版日期2013
• 单位天水师范学院